Implementation of adomian polynomials in variational iteration method for solving volterra integral equations

  • Abstract
  • Keywords
  • References
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  • Abstract

    In this paper Adomian polynomials are employed is solving Variational Iteration Method for finding Volterra integral equations. The proposed technique involves Adomian Polynomials in the correction functional equation. The solutions have been found by suggested iterative scheme without any discretization, linearization, or restrictive assumptions, and it is quite efficient and is practically well suited. Two examples are given to verify the reliability and the efficiency of this method.

    Keywords: Variational Iteration Method, Adomian Polynomials, Volterra Integral Equations, Functional Equation.

  • References

    1. J. H. He, "Some asymptotic methods for strongly nonlinear equation", Int. J. Mod. Phys., 10 (20) (2006) 1144-1199.
    2. J. H. He, "Homotopy perturbation technique", Comput. Math. Appl. Mech, Energy, 178 (1999) 178-257.
    3. J. H. He, "Homotopy perturbation method for solving boundary value problems", Phys. Lett A, 350 (2006) 87-88.
    4. J. H. He, "Comparison of homotopy perturbation method and homotopy analysis method", Appl. Math. Comput, 156 (2004) 527-539.
    5. J. H. He, "Homotopy perturbation method for bifurcation of nonlinear problems", Int. J. Nonlin. Sci Num. Simul, 6 (2) (2005) 207-208.
    6. J. H. He, "Variational iteration method. A kind of non-linear analytical technique, some examples", Internat. J. Nonlinear Mech, 34 (4) (1999) 699-708. (98)00048-1.
    7. J. H. He, "Variational iteration method for autonomous ordinary differential systems", Appl. Math. Comput., 114 (2-3) (2000) 115-123. (99)00104-6.
    8. J. H. He, X. H. Wu, "Construction of solitary solution and compaction-like solution by variational iteration method", Chaos, Solitons and Fractals, 29 (1) (226) 108-113.
    9. J. H. He, "Variational iteration method- Some recent results and new interpretations", J. Comput. Appl. Math, 207 (2007) 3-17.
    10. J. H. He, X. H. Wu, "Variational iteration method: New development and applications", Comput. Math. Appl, 54 (2007) 881-894.
    11. M. Inokuti, H. Sekine,T. Mura, "General use of the Lagrange multiplier in non-linear mathematical physics, in: S. Nemat-Nasser (Ed.),Variational Method in the Mechanics of Solids", Pergamon Press, Oxford, 1978, 156162.




Article ID: 3013
DOI: 10.14419/gjma.v2i3.3013

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